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%I #13 Jul 31 2020 14:14:54
%S 29,569,1289,41609,147449,2322569,2842589,7096889,7485689,10074269,
%T 16208669,21288989,33802589,54819209,56610569,57699209,59814749,
%U 115218749,118069949,126427529,134235389,149670749,196448249,240746249
%N List of primes p with following properties: p = prime(n-1) for some n, p+7 is a square and is equal to prime(n+1)-1.
%C Conjecture: If the condition holds, prime(n-1) and prime(n) are twin primes of the form 10k+9 and 10k1+1, i.e. the last digits of the twin prime pairs are 9 and 1. The 9 ending is evident in this sequence. The table of the first 101 terms was computed using Zak Seidov's table.
%H Cino Hilliard, <a href="/A158529/b158529.txt">List of n, a(n) for n=1..101</a>
%H S. M. Ruiz, <a href="http://groups.yahoo.com/group/primenumbers/message/19899">Integer then equal</a>.
%H Sebastian Martin Ruiz and others, <a href="/A158460/a158460.txt">Integers then Equals</a>, digest of 7 messages in primenumbers Yahoo group, Mar 14 - Mar 20, 2009.
%H Zak Seidov, <a href="http://zak08.livejournal.com/7702.html">A158470 first 101 terms</a>.
%F Prime(n) is the n-th prime number.
%e For n = 11, prime(11-1)=29, 29+7=36; prime(11+1)=37, 37-1=36. So 29 is the first entry in the sequence.
%t ppQ[{a_,b_}]:=Module[{s=Prime[a+1]-1},IntegerQ[Sqrt[s]]&&b+7==s]; Select[ Table[ {n,Prime[n-1]},{n,2,133*10^5}],ppQ][[All,2]] (* _Harvey P. Dale_, Jul 31 2020 *)
%o (PARI) \\Copy and paste the Zak's file to zaklist.txt and edit to a straight
%o \\list with CR after each entry. Start a new Pari sesion then \r zakilist.txt
%o integerequal(a,b) =
%o {
%o local(x,p1,p2);
%o for(j=1,101,
%o x=eval(concat("%",j)); p1=prime2(x-1);
%o if(issquare(p1+a),
%o p2=prime2(x+1);if((p1+a)==(p2-b),
%o print1(p1",")
%o )
%o prime2(n) = \\the n-th prime using c:\sieve\prime.exe calling 8byte binary
%o \\g:\sievedata\prime2-1trill.bin" 300 gig file of primes <10^12
%o {
%o local(x,s);
%o s=concat("c:/sieve/prime ",Str(n));
%o s=concat(s," > temp.txt");
%o \\Must save to a temp file for correct output
%o system(s);
%o return(read("temp.txt"))
%o }
%o )
%o )
%o }
%K nonn
%O 1,1
%A _Cino Hilliard_, Mar 20 2009
%E Edited by _N. J. A. Sloane_ Aug 31 2009 (rephrased definition, corrected offset).
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